Abstract

We have experimentally investigated the meaning of the effective optical absorption [μa (eff)] and the reduced scattering [μs(eff)] coefficients measured on the surfaces of two-layered turbid media, using the diffusion equation for homogeneous, semi-infinite media. We performed frequency-domain spectroscopy in a reflectance geometry, using source–detector distances in the range 1.5–4.5 cm. We measured 100 samples, each made of one layer (thickness in the range 0.08–1.6 cm) on top of one semi-infinite block. The optical properties of the samples were similar to those of soft tissues in the near infrared. We found that the measured effective optical coefficients are representative of the underlying block if the superficial layer is less than ∼0.4 cm thick, whereas they are representative of the superficial layer if it is more than ∼1.3 cm thick.

© 1998 Optical Society of America

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1998

1997

1996

S. Homma, T. Fukunaga, A. Kagaya, “Influence of adipose tissue thickness on near infrared spectroscopic signals in the measurement of human muscle,” J. Biomed. Opt. 1, 418–424 (1996).
[CrossRef] [PubMed]

1995

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. M. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for non-invasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

M. S. Patterson, S. Andersson-Engels, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,” Appl. Opt. 34, 22–30 (1995).
[CrossRef] [PubMed]

1994

1993

A. D. Edwards, C. Richardson, P. Van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. R. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

R. A. de Blasi, M. Cope, C. Elwell, F. Safoue, M. Ferrari, “Non invasive measurement of human forearm oxygen consumption by near infrared spectroscopy,” Eur. J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
[CrossRef] [PubMed]

1992

I. Dayan, S. Havlin, G. H. Weiss, “Photon migration in a two-layer turbid medium: a diffusion analysis,” J. Mod. Opt. 39, 1567–1582 (1992).
[CrossRef]

1990

1989

1988

1985

H. Wallberg, A. Alveryd, K. Nasiell, P. Sundelin, U. Bergvall, S. Troell, “Diaphanography in benign breast disorders: correlation with clinical examination, mammography, cytology and histology,” Acta Radiol. Diagn. 26, 129–136 (1985).

Alveryd, A.

H. Wallberg, A. Alveryd, K. Nasiell, P. Sundelin, U. Bergvall, S. Troell, “Diaphanography in benign breast disorders: correlation with clinical examination, mammography, cytology and histology,” Acta Radiol. Diagn. 26, 129–136 (1985).

Anderson, E. R.

Andersson-Engels, S.

Arridge, S. R.

M. Cope, P. van der Zee, M. Essenpreis, S. R. Arridge, D. T. Delpy, “Data analysis methods for near infrared spectroscopy of tissues: problems in determining the relative cytochrome aa3 concentration,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 251–263 (1991).

Barbieri, B.

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for non-invasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light-emitting-diode based technique,” Appl. Opt. 33, 5204–5213 (1994).
[CrossRef] [PubMed]

M. A. Franceschini, D. Wallace, B. Barbieri, S. Fantini, W. W. Mantulin, S. Pratesi, G. P. Donzelli, E. Gratton, “Optical study of the skeletal muscle during exercise with a second generation frequency-domain tissue oximeter,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 807–814 (1997).
[CrossRef]

Bays, R.

Berger, M.

Bergvall, U.

H. Wallberg, A. Alveryd, K. Nasiell, P. Sundelin, U. Bergvall, S. Troell, “Diaphanography in benign breast disorders: correlation with clinical examination, mammography, cytology and histology,” Acta Radiol. Diagn. 26, 129–136 (1985).

Böcker, D.

Bonner, R.

Brenner, M.

Bruulsema, J. T.

Cerussi, A.

A. Cerussi, J. Maier, S. Fantini, M. A. Franceschini, E. Gratton, “The frequency-domain multi-distance method in the presence of curved boundaries,” OSA Trends in Optics and Photonics on Biomedical Optical Spectroscopy and Diagnostics, E. Sevick-Muraca, D. Benaron, eds., Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 92–97.

Chance, B.

S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

A. H. Hielscher, H. Liu, L. Wang, F. K. Tittel, B. Chance, S. L. Jacques, “Determination of blood oxygenation in the brain by time resolved reflectance spectroscopy. I. Influence of the skin, skull, and meninges,” in Biochemical Diagnostic Instrumentation, R. F. Bonner, G. E. Cohn, T. M. Laue, A. V. Priezzhev, eds., Proc. SPIE2136, 15–25 (1994).
[CrossRef]

M. Miwa, Y. Ueda, B. Chance, “Development of time resolved spectroscopy system for quantitative non-invasive tissue measurement,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 142–149 (1995).
[CrossRef]

Cope, M.

M. Kohl, M. Cope, M. Essenpreis, D. Böcker, “Influence of glucose concentration on light scattering in tissue-simulating phantoms,” Opt. Lett. 19, 2170–2172 (1994).
[CrossRef] [PubMed]

A. D. Edwards, C. Richardson, P. Van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. R. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

R. A. de Blasi, M. Cope, C. Elwell, F. Safoue, M. Ferrari, “Non invasive measurement of human forearm oxygen consumption by near infrared spectroscopy,” Eur. J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

M. Cope, P. van der Zee, M. Essenpreis, S. R. Arridge, D. T. Delpy, “Data analysis methods for near infrared spectroscopy of tissues: problems in determining the relative cytochrome aa3 concentration,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 251–263 (1991).

Coquoz, O.

Corballis, P. M.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. M. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef]

Dayan, I.

I. Dayan, S. Havlin, G. H. Weiss, “Photon migration in a two-layer turbid medium: a diffusion analysis,” J. Mod. Opt. 39, 1567–1582 (1992).
[CrossRef]

de Blasi, R. A.

R. A. de Blasi, M. Cope, C. Elwell, F. Safoue, M. Ferrari, “Non invasive measurement of human forearm oxygen consumption by near infrared spectroscopy,” Eur. J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

Delpy, D. T.

A. D. Edwards, C. Richardson, P. Van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. R. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

M. Cope, P. van der Zee, M. Essenpreis, S. R. Arridge, D. T. Delpy, “Data analysis methods for near infrared spectroscopy of tissues: problems in determining the relative cytochrome aa3 concentration,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 251–263 (1991).

Dögnitz, N.

Donzelli, G. P.

M. A. Franceschini, D. Wallace, B. Barbieri, S. Fantini, W. W. Mantulin, S. Pratesi, G. P. Donzelli, E. Gratton, “Optical study of the skeletal muscle during exercise with a second generation frequency-domain tissue oximeter,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 807–814 (1997).
[CrossRef]

Edwards, A. D.

A. D. Edwards, C. Richardson, P. Van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. R. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Elwell, C.

A. D. Edwards, C. Richardson, P. Van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. R. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

R. A. de Blasi, M. Cope, C. Elwell, F. Safoue, M. Ferrari, “Non invasive measurement of human forearm oxygen consumption by near infrared spectroscopy,” Eur. J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

Essenpreis, M.

Fabiani, M.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. M. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef]

Fantini, S.

S. Fantini, M. A. Franceschini, E. Gratton, “Effective source term in the diffusion equation for photon transport in turbid media,” Appl. Opt. 36, 156–163 (1997).
[CrossRef] [PubMed]

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for non-invasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. M. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef]

J. S. Maier, S. A. Walker, S. Fantini, M. A. Franceschini, E. Gratton, “Possible correlation between blood glucose concentration and the reduced scattering coefficient of tissues in the near infrared,” Opt. Lett. 19, 2062–2064 (1994).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994).
[CrossRef]

S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light-emitting-diode based technique,” Appl. Opt. 33, 5204–5213 (1994).
[CrossRef] [PubMed]

M. A. Franceschini, S. Fantini, S. A. Walker, J. S. Maier, W. W. Mantulin, E. Gratton, “Multi-channel optical instrument for near-infrared imaging of tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds. Proc. SPIE2389, 264–273 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, S. A. Walker, J. S. Maier, E. Gratton, “Photon path distributions in turbid media: applications for imaging,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 340–349 (1995).
[CrossRef]

A. Cerussi, J. Maier, S. Fantini, M. A. Franceschini, E. Gratton, “The frequency-domain multi-distance method in the presence of curved boundaries,” OSA Trends in Optics and Photonics on Biomedical Optical Spectroscopy and Diagnostics, E. Sevick-Muraca, D. Benaron, eds., Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 92–97.

M. A. Franceschini, D. Wallace, B. Barbieri, S. Fantini, W. W. Mantulin, S. Pratesi, G. P. Donzelli, E. Gratton, “Optical study of the skeletal muscle during exercise with a second generation frequency-domain tissue oximeter,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 807–814 (1997).
[CrossRef]

V. Quaresima, M. A. Franceschini, S. Fantini, E. Gratton, M. Ferrari, “Difference in leg muscles oxygenation during treadmill exercise by a new near infrared frequency-domain oximeter,” in Photon Propagation in Tissues III, D. A. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 116–120 (1998).
[CrossRef]

Farrel, T. J.

Ferrari, M.

R. A. de Blasi, M. Cope, C. Elwell, F. Safoue, M. Ferrari, “Non invasive measurement of human forearm oxygen consumption by near infrared spectroscopy,” Eur. J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

V. Quaresima, M. A. Franceschini, S. Fantini, E. Gratton, M. Ferrari, “Difference in leg muscles oxygenation during treadmill exercise by a new near infrared frequency-domain oximeter,” in Photon Propagation in Tissues III, D. A. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 116–120 (1998).
[CrossRef]

Fishkin, J. B.

Franceschini, M. A.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, E. Gratton, “Effective source term in the diffusion equation for photon transport in turbid media,” Appl. Opt. 36, 156–163 (1997).
[CrossRef] [PubMed]

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. M. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for non-invasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light-emitting-diode based technique,” Appl. Opt. 33, 5204–5213 (1994).
[CrossRef] [PubMed]

J. S. Maier, S. A. Walker, S. Fantini, M. A. Franceschini, E. Gratton, “Possible correlation between blood glucose concentration and the reduced scattering coefficient of tissues in the near infrared,” Opt. Lett. 19, 2062–2064 (1994).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994).
[CrossRef]

M. A. Franceschini, D. Wallace, B. Barbieri, S. Fantini, W. W. Mantulin, S. Pratesi, G. P. Donzelli, E. Gratton, “Optical study of the skeletal muscle during exercise with a second generation frequency-domain tissue oximeter,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 807–814 (1997).
[CrossRef]

V. Quaresima, M. A. Franceschini, S. Fantini, E. Gratton, M. Ferrari, “Difference in leg muscles oxygenation during treadmill exercise by a new near infrared frequency-domain oximeter,” in Photon Propagation in Tissues III, D. A. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 116–120 (1998).
[CrossRef]

M. A. Franceschini, S. Fantini, S. A. Walker, J. S. Maier, W. W. Mantulin, E. Gratton, “Multi-channel optical instrument for near-infrared imaging of tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds. Proc. SPIE2389, 264–273 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, S. A. Walker, J. S. Maier, E. Gratton, “Photon path distributions in turbid media: applications for imaging,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 340–349 (1995).
[CrossRef]

A. Cerussi, J. Maier, S. Fantini, M. A. Franceschini, E. Gratton, “The frequency-domain multi-distance method in the presence of curved boundaries,” OSA Trends in Optics and Photonics on Biomedical Optical Spectroscopy and Diagnostics, E. Sevick-Muraca, D. Benaron, eds., Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 92–97.

Friedman, D.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. M. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef]

Fukunaga, T.

S. Homma, T. Fukunaga, A. Kagaya, “Influence of adipose tissue thickness on near infrared spectroscopic signals in the measurement of human muscle,” J. Biomed. Opt. 1, 418–424 (1996).
[CrossRef] [PubMed]

Gaida, G.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Gopinath, S. P.

S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
[CrossRef] [PubMed]

Gratton, E.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, E. Gratton, “Effective source term in the diffusion equation for photon transport in turbid media,” Appl. Opt. 36, 156–163 (1997).
[CrossRef] [PubMed]

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. M. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for non-invasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light-emitting-diode based technique,” Appl. Opt. 33, 5204–5213 (1994).
[CrossRef] [PubMed]

J. S. Maier, S. A. Walker, S. Fantini, M. A. Franceschini, E. Gratton, “Possible correlation between blood glucose concentration and the reduced scattering coefficient of tissues in the near infrared,” Opt. Lett. 19, 2062–2064 (1994).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, E. Gratton, “Semi-infinite-geometry boundary problem for light migration in highly scattering media: a frequency-domain study in the diffusion approximation,” J. Opt. Soc. Am. B 11, 2128–2138 (1994).
[CrossRef]

M. A. Franceschini, D. Wallace, B. Barbieri, S. Fantini, W. W. Mantulin, S. Pratesi, G. P. Donzelli, E. Gratton, “Optical study of the skeletal muscle during exercise with a second generation frequency-domain tissue oximeter,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 807–814 (1997).
[CrossRef]

V. Quaresima, M. A. Franceschini, S. Fantini, E. Gratton, M. Ferrari, “Difference in leg muscles oxygenation during treadmill exercise by a new near infrared frequency-domain oximeter,” in Photon Propagation in Tissues III, D. A. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 116–120 (1998).
[CrossRef]

M. A. Franceschini, S. Fantini, S. A. Walker, J. S. Maier, W. W. Mantulin, E. Gratton, “Multi-channel optical instrument for near-infrared imaging of tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds. Proc. SPIE2389, 264–273 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, S. A. Walker, J. S. Maier, E. Gratton, “Photon path distributions in turbid media: applications for imaging,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 340–349 (1995).
[CrossRef]

A. Cerussi, J. Maier, S. Fantini, M. A. Franceschini, E. Gratton, “The frequency-domain multi-distance method in the presence of curved boundaries,” OSA Trends in Optics and Photonics on Biomedical Optical Spectroscopy and Diagnostics, E. Sevick-Muraca, D. Benaron, eds., Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 92–97.

Gratton, G.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. M. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef]

Grossman, R. G.

S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
[CrossRef] [PubMed]

Hampson, N. B.

N. B. Hampson, C. A. Piantadosi, “Near infrared monitoring of human skeletal muscle oxygenation during forearm ischemia,” J. Appl. Physiol. 64, 2449–2457 (1988).
[PubMed]

Havlin, S.

Hayward, J. E.

Heinemann, L.

Hielscher, A. H.

A. H. Hielscher, H. Liu, L. Wang, F. K. Tittel, B. Chance, S. L. Jacques, “Determination of blood oxygenation in the brain by time resolved reflectance spectroscopy. I. Influence of the skin, skull, and meninges,” in Biochemical Diagnostic Instrumentation, R. F. Bonner, G. E. Cohn, T. M. Laue, A. V. Priezzhev, eds., Proc. SPIE2136, 15–25 (1994).
[CrossRef]

Homma, S.

S. Homma, T. Fukunaga, A. Kagaya, “Influence of adipose tissue thickness on near infrared spectroscopic signals in the measurement of human muscle,” J. Biomed. Opt. 1, 418–424 (1996).
[CrossRef] [PubMed]

Jacques, S. L.

A. H. Hielscher, H. Liu, L. Wang, F. K. Tittel, B. Chance, S. L. Jacques, “Determination of blood oxygenation in the brain by time resolved reflectance spectroscopy. I. Influence of the skin, skull, and meninges,” in Biochemical Diagnostic Instrumentation, R. F. Bonner, G. E. Cohn, T. M. Laue, A. V. Priezzhev, eds., Proc. SPIE2136, 15–25 (1994).
[CrossRef]

Jess, H.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Kagaya, A.

S. Homma, T. Fukunaga, A. Kagaya, “Influence of adipose tissue thickness on near infrared spectroscopic signals in the measurement of human muscle,” J. Biomed. Opt. 1, 418–424 (1996).
[CrossRef] [PubMed]

Kaneko, M.

Y. Yamashita, M. Kaneko, “Visible and infrared diaphanoscopy for medical diagnosis,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Muller, ed. (SPIE, Bellingham, Wash.1993), pp. 283–316.

Kaschke, M.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Keijzer, M.

Kiefer, J.

Kienle, A.

Kohl, M.

Koschinsky, T.

Liu, H.

A. H. Hielscher, H. Liu, L. Wang, F. K. Tittel, B. Chance, S. L. Jacques, “Determination of blood oxygenation in the brain by time resolved reflectance spectroscopy. I. Influence of the skin, skull, and meninges,” in Biochemical Diagnostic Instrumentation, R. F. Bonner, G. E. Cohn, T. M. Laue, A. V. Priezzhev, eds., Proc. SPIE2136, 15–25 (1994).
[CrossRef]

Maier, J.

A. Cerussi, J. Maier, S. Fantini, M. A. Franceschini, E. Gratton, “The frequency-domain multi-distance method in the presence of curved boundaries,” OSA Trends in Optics and Photonics on Biomedical Optical Spectroscopy and Diagnostics, E. Sevick-Muraca, D. Benaron, eds., Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 92–97.

Maier, J. S.

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for non-invasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

J. S. Maier, S. A. Walker, S. Fantini, M. A. Franceschini, E. Gratton, “Possible correlation between blood glucose concentration and the reduced scattering coefficient of tissues in the near infrared,” Opt. Lett. 19, 2062–2064 (1994).
[CrossRef] [PubMed]

M. A. Franceschini, S. Fantini, S. A. Walker, J. S. Maier, W. W. Mantulin, E. Gratton, “Multi-channel optical instrument for near-infrared imaging of tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds. Proc. SPIE2389, 264–273 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, S. A. Walker, J. S. Maier, E. Gratton, “Photon path distributions in turbid media: applications for imaging,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 340–349 (1995).
[CrossRef]

Mantulin, W. W.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

M. A. Franceschini, S. Fantini, S. A. Walker, J. S. Maier, W. W. Mantulin, E. Gratton, “Multi-channel optical instrument for near-infrared imaging of tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds. Proc. SPIE2389, 264–273 (1995).
[CrossRef]

M. A. Franceschini, D. Wallace, B. Barbieri, S. Fantini, W. W. Mantulin, S. Pratesi, G. P. Donzelli, E. Gratton, “Optical study of the skeletal muscle during exercise with a second generation frequency-domain tissue oximeter,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 807–814 (1997).
[CrossRef]

Miwa, M.

M. Miwa, Y. Ueda, B. Chance, “Development of time resolved spectroscopy system for quantitative non-invasive tissue measurement,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 142–149 (1995).
[CrossRef]

Moesta, K. T.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Nasiell, K.

H. Wallberg, A. Alveryd, K. Nasiell, P. Sundelin, U. Bergvall, S. Troell, “Diaphanography in benign breast disorders: correlation with clinical examination, mammography, cytology and histology,” Acta Radiol. Diagn. 26, 129–136 (1985).

Nossal, R.

Orskov, H.

Osei, E. K.

Patterson, M. S.

Piantadosi, C. A.

N. B. Hampson, C. A. Piantadosi, “Near infrared monitoring of human skeletal muscle oxygenation during forearm ischemia,” J. Appl. Physiol. 64, 2449–2457 (1988).
[PubMed]

Pratesi, S.

M. A. Franceschini, D. Wallace, B. Barbieri, S. Fantini, W. W. Mantulin, S. Pratesi, G. P. Donzelli, E. Gratton, “Optical study of the skeletal muscle during exercise with a second generation frequency-domain tissue oximeter,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 807–814 (1997).
[CrossRef]

Quaresima, V.

V. Quaresima, M. A. Franceschini, S. Fantini, E. Gratton, M. Ferrari, “Difference in leg muscles oxygenation during treadmill exercise by a new near infrared frequency-domain oximeter,” in Photon Propagation in Tissues III, D. A. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 116–120 (1998).
[CrossRef]

Reynolds, E. O. R.

A. D. Edwards, C. Richardson, P. Van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. R. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Richardson, C.

A. D. Edwards, C. Richardson, P. Van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. R. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Robertson, C. S.

S. P. Gopinath, C. S. Robertson, R. G. Grossman, B. Chance, “Near-infrared spectroscopic localization of intracranial hematomas,” J. Neurosurg. 79, 43–47 (1993).
[CrossRef] [PubMed]

Safoue, F.

R. A. de Blasi, M. Cope, C. Elwell, F. Safoue, M. Ferrari, “Non invasive measurement of human forearm oxygen consumption by near infrared spectroscopy,” Eur. J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

Sandahl-Christiansen, J.

Schlag, P. M.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Schmelzeisen-Redeker, G.

Schmitt, J. M.

Seeber, M.

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
[CrossRef] [PubMed]

Star, W. M.

Storchi, P. R. M.

Sundelin, P.

H. Wallberg, A. Alveryd, K. Nasiell, P. Sundelin, U. Bergvall, S. Troell, “Diaphanography in benign breast disorders: correlation with clinical examination, mammography, cytology and histology,” Acta Radiol. Diagn. 26, 129–136 (1985).

Taitelbaum, H.

Tittel, F. K.

A. H. Hielscher, H. Liu, L. Wang, F. K. Tittel, B. Chance, S. L. Jacques, “Determination of blood oxygenation in the brain by time resolved reflectance spectroscopy. I. Influence of the skin, skull, and meninges,” in Biochemical Diagnostic Instrumentation, R. F. Bonner, G. E. Cohn, T. M. Laue, A. V. Priezzhev, eds., Proc. SPIE2136, 15–25 (1994).
[CrossRef]

Troell, S.

H. Wallberg, A. Alveryd, K. Nasiell, P. Sundelin, U. Bergvall, S. Troell, “Diaphanography in benign breast disorders: correlation with clinical examination, mammography, cytology and histology,” Acta Radiol. Diagn. 26, 129–136 (1985).

Tromberg, B. J.

Ueda, Y.

M. Miwa, Y. Ueda, B. Chance, “Development of time resolved spectroscopy system for quantitative non-invasive tissue measurement,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 142–149 (1995).
[CrossRef]

van den Bergh, H.

Van der Zee, P.

A. D. Edwards, C. Richardson, P. Van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. R. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

M. Cope, P. van der Zee, M. Essenpreis, S. R. Arridge, D. T. Delpy, “Data analysis methods for near infrared spectroscopy of tissues: problems in determining the relative cytochrome aa3 concentration,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 251–263 (1991).

Wagnières, G.

Walker, E. C.

Walker, S. A.

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for non-invasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
[CrossRef]

J. S. Maier, S. A. Walker, S. Fantini, M. A. Franceschini, E. Gratton, “Possible correlation between blood glucose concentration and the reduced scattering coefficient of tissues in the near infrared,” Opt. Lett. 19, 2062–2064 (1994).
[CrossRef] [PubMed]

M. A. Franceschini, S. Fantini, S. A. Walker, J. S. Maier, W. W. Mantulin, E. Gratton, “Multi-channel optical instrument for near-infrared imaging of tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds. Proc. SPIE2389, 264–273 (1995).
[CrossRef]

S. Fantini, M. A. Franceschini, S. A. Walker, J. S. Maier, E. Gratton, “Photon path distributions in turbid media: applications for imaging,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 340–349 (1995).
[CrossRef]

Wall, R. T.

Wallace, D.

M. A. Franceschini, D. Wallace, B. Barbieri, S. Fantini, W. W. Mantulin, S. Pratesi, G. P. Donzelli, E. Gratton, “Optical study of the skeletal muscle during exercise with a second generation frequency-domain tissue oximeter,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 807–814 (1997).
[CrossRef]

Wallberg, H.

H. Wallberg, A. Alveryd, K. Nasiell, P. Sundelin, U. Bergvall, S. Troell, “Diaphanography in benign breast disorders: correlation with clinical examination, mammography, cytology and histology,” Acta Radiol. Diagn. 26, 129–136 (1985).

Wang, L.

A. H. Hielscher, H. Liu, L. Wang, F. K. Tittel, B. Chance, S. L. Jacques, “Determination of blood oxygenation in the brain by time resolved reflectance spectroscopy. I. Influence of the skin, skull, and meninges,” in Biochemical Diagnostic Instrumentation, R. F. Bonner, G. E. Cohn, T. M. Laue, A. V. Priezzhev, eds., Proc. SPIE2136, 15–25 (1994).
[CrossRef]

Weiss, G. H.

Wilson, B. C.

Wyatt, J. S.

A. D. Edwards, C. Richardson, P. Van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. R. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

Yamashita, Y.

Y. Yamashita, M. Kaneko, “Visible and infrared diaphanoscopy for medical diagnosis,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Muller, ed. (SPIE, Bellingham, Wash.1993), pp. 283–316.

Zhou, G. X.

Acta Radiol. Diagn.

H. Wallberg, A. Alveryd, K. Nasiell, P. Sundelin, U. Bergvall, S. Troell, “Diaphanography in benign breast disorders: correlation with clinical examination, mammography, cytology and histology,” Acta Radiol. Diagn. 26, 129–136 (1985).

Appl. Opt.

M. Keijzer, W. M. Star, P. R. M. Storchi, “Optical diffusion in layered media,” Appl. Opt. 27, 1820–1824 (1988).
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R. Nossal, J. Kiefer, G. H. Weiss, R. Bonner, H. Taitelbaum, S. Havlin, “Photon migration in layered media,” Appl. Opt. 27, 3382–3391 (1988).
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H. Taitelbaum, S. Havlin, G. H. Weiss, “Tissue characterization and imaging using photon density waves,” Appl. Opt. 28, 2245–2249 (1989).
[CrossRef] [PubMed]

M. S. Patterson, B. Chance, B. C. Wilson, “Time resolved reflectance and transmittance for the non-invasive measurement of optical properties,” Appl. Opt. 28, 2331–2336 (1989).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, J. B. Fishkin, B. Barbieri, E. Gratton, “Quantitative determination of the absorption spectra of chromophores in strongly scattering media: a light-emitting-diode based technique,” Appl. Opt. 33, 5204–5213 (1994).
[CrossRef] [PubMed]

J. B. Fishkin, O. Coquoz, E. R. Anderson, M. Brenner, B. J. Tromberg, “Frequency-domain photon migration measurements of normal and malignant tissue optical properties in a human subject,” Appl. Opt. 36, 10–20 (1997).
[CrossRef] [PubMed]

S. Fantini, M. A. Franceschini, E. Gratton, “Effective source term in the diffusion equation for photon transport in turbid media,” Appl. Opt. 36, 156–163 (1997).
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T. J. Farrel, M. S. Patterson, M. Essenpreis, “Influence of layered tissue architecture on estimates of tissue optical properties obtained from spatially resolved diffuse reflectometry,” Appl. Opt. 37, 1958–1972 (1998).
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M. S. Patterson, S. Andersson-Engels, B. C. Wilson, E. K. Osei, “Absorption spectroscopy in tissue-simulating materials: a theoretical and experimental study of photon paths,” Appl. Opt. 34, 22–30 (1995).
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A. Kienle, M. S. Patterson, N. Dögnitz, R. Bays, G. Wagnières, H. van den Bergh, “Noninvasive determination of the optical properties of two-layered turbid media,” Appl. Opt. 37, 779–791 (1998).
[CrossRef]

Eur. J. Appl. Physiol.

R. A. de Blasi, M. Cope, C. Elwell, F. Safoue, M. Ferrari, “Non invasive measurement of human forearm oxygen consumption by near infrared spectroscopy,” Eur. J. Appl. Physiol. 67, 20–25 (1993).
[CrossRef]

J. Appl. Physiol.

N. B. Hampson, C. A. Piantadosi, “Near infrared monitoring of human skeletal muscle oxygenation during forearm ischemia,” J. Appl. Physiol. 64, 2449–2457 (1988).
[PubMed]

A. D. Edwards, C. Richardson, P. Van der Zee, C. Elwell, J. S. Wyatt, M. Cope, D. T. Delpy, E. O. R. Reynolds, “Measurement of hemoglobin flow and blood flow by near-infrared spectroscopy,” J. Appl. Physiol. 75, 1884–1889 (1993).
[PubMed]

J. Biomed. Opt.

S. Homma, T. Fukunaga, A. Kagaya, “Influence of adipose tissue thickness on near infrared spectroscopic signals in the measurement of human muscle,” J. Biomed. Opt. 1, 418–424 (1996).
[CrossRef] [PubMed]

J. Cogn. Neurosci.

G. Gratton, M. Fabiani, D. Friedman, M. A. Franceschini, S. Fantini, P. M. Corballis, E. Gratton, “Rapid changes of optical parameters in the human brain during a tapping task,” J. Cogn. Neurosci. 7, 446–456 (1995).
[CrossRef]

J. Mod. Opt.

I. Dayan, S. Havlin, G. H. Weiss, “Photon migration in a two-layer turbid medium: a diffusion analysis,” J. Mod. Opt. 39, 1567–1582 (1992).
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J. Opt. Soc. Am. A

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Opt. Eng.

S. Fantini, M. A. Franceschini, J. S. Maier, S. A. Walker, B. Barbieri, E. Gratton, “Frequency-domain multichannel optical detector for non-invasive tissue spectroscopy and oximetry,” Opt. Eng. 34, 32–42 (1995).
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Proc. Natl. Acad. Sci. USA

M. A. Franceschini, K. T. Moesta, S. Fantini, G. Gaida, E. Gratton, H. Jess, W. W. Mantulin, M. Seeber, P. M. Schlag, M. Kaschke, “Frequency-domain techniques enhance optical mammography: initial clinical results,” Proc. Natl. Acad. Sci. USA 94, 6468–6473 (1997).
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M. Miwa, Y. Ueda, B. Chance, “Development of time resolved spectroscopy system for quantitative non-invasive tissue measurement,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 142–149 (1995).
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A. H. Hielscher, H. Liu, L. Wang, F. K. Tittel, B. Chance, S. L. Jacques, “Determination of blood oxygenation in the brain by time resolved reflectance spectroscopy. I. Influence of the skin, skull, and meninges,” in Biochemical Diagnostic Instrumentation, R. F. Bonner, G. E. Cohn, T. M. Laue, A. V. Priezzhev, eds., Proc. SPIE2136, 15–25 (1994).
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A. Cerussi, J. Maier, S. Fantini, M. A. Franceschini, E. Gratton, “The frequency-domain multi-distance method in the presence of curved boundaries,” OSA Trends in Optics and Photonics on Biomedical Optical Spectroscopy and Diagnostics, E. Sevick-Muraca, D. Benaron, eds., Vol. 3 of OSA Trends in Optics and Photonics Series (Optical Society of America, Washington, D.C., 1996), pp. 92–97.

M. A. Franceschini, D. Wallace, B. Barbieri, S. Fantini, W. W. Mantulin, S. Pratesi, G. P. Donzelli, E. Gratton, “Optical study of the skeletal muscle during exercise with a second generation frequency-domain tissue oximeter,” in Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, B. Chance, R. R. Alfano, eds., Proc. SPIE2979, 807–814 (1997).
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M. A. Franceschini, S. Fantini, S. A. Walker, J. S. Maier, W. W. Mantulin, E. Gratton, “Multi-channel optical instrument for near-infrared imaging of tissue,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds. Proc. SPIE2389, 264–273 (1995).
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M. Cope, P. van der Zee, M. Essenpreis, S. R. Arridge, D. T. Delpy, “Data analysis methods for near infrared spectroscopy of tissues: problems in determining the relative cytochrome aa3 concentration,” in Time-Resolved Spectroscopy and Imaging of Tissues, B. Chance, ed., Proc. SPIE1431, 251–263 (1991).

S. Fantini, M. A. Franceschini, S. A. Walker, J. S. Maier, E. Gratton, “Photon path distributions in turbid media: applications for imaging,” in Optical Tomography, Photon Migration, and Spectroscopy of Tissue and Model Media: Theory, Human Studies, and Instrumentation, B. Chance, R. R. Alfano, eds., Proc. SPIE2389, 340–349 (1995).
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V. Quaresima, M. A. Franceschini, S. Fantini, E. Gratton, M. Ferrari, “Difference in leg muscles oxygenation during treadmill exercise by a new near infrared frequency-domain oximeter,” in Photon Propagation in Tissues III, D. A. Benaron, B. Chance, M. Ferrari, eds., Proc. SPIE3194, 116–120 (1998).
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Y. Yamashita, M. Kaneko, “Visible and infrared diaphanoscopy for medical diagnosis,” in Medical Optical Tomography: Functional Imaging and Monitoring, G. J. Muller, ed. (SPIE, Bellingham, Wash.1993), pp. 283–316.

B. Chance, R. R. Alfano, eds., Optical Tomography and Spectroscopy of Tissue: Theory, Instrumentation, Model, and Human Studies II, Proc. SPIE2979 (1997).

D. A. Benaron, B. Chance, M. Ferrari, eds., Photon Propagation in Tissues III, Proc. SPIE3194 (1998).

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Figures (9)

Fig. 1
Fig. 1

Effectively semi-infinite blocks and layers employed in our experimental study. The blocks and the layers are composed of five batches of gelatin (labeled 1–5), each having a different amount of TiO2 particles and black India ink. The optical properties of each batch at 750 nm are indicated inside the blocks. The numbers in parentheses give the error in the last digit of the corresponding parameter. The thickness of each block and layer is also shown. We carried out measurements on all the 100 combinations of one layer on top of one block.

Fig. 2
Fig. 2

Experimental arrangement. The frequency-domain data (dc, ac, and phase) were measured on top of the layer–block combination over the range of distances 1.5–3.0 cm (channel a) and 3.0–4.5 cm (channel b). PMT’s, photomultiplier tubes; 110 MHz is the modulation frequency of the intensity of the light sources.

Fig. 3
Fig. 3

Dependence of ln(r 2 dc) on source–detector distance for five different media. Thick lines, semi-infinite, homogeneous media that have either the layer optical coefficients [upper curve, μ a (L) = 0.017 cm-1, μ s (L) = 5.4 cm-1] or the block optical coefficients [lower curve, μ a (B) = 0.070 cm-1, μ s (B) = 7.3 cm-1]. Thin lines, three layer–block configurations that differ in layer thickness. The layer thickness is indicated next to each line. The media considered in this figure are less attenuating than those employed in our experimental study. The lines in this figure were calculated from the solution of diffusion theory for two-layered media reported by Kienle et al.23

Fig. 4
Fig. 4

Squares and circles, the values of the functions f[ r, dc, μ a (eff), μ s (eff)] and h[ r, Φ, μ a (eff), μ s (eff)], respectively, versus source–detector distance r. As discussed in the text, the fact that f and h are approximately described by straight lines (the dashed lines are the best-fit straight lines through the points) allows us to apply the frequency-domain multidistance method to obtain the effective optical properties μ a (eff) and μ s (eff). (a) Layer thickness, 0.18 cm; (b) layer thickness 1.3 cm. (a), (b) Layer optical properties are μ a (L4) = 0.072 cm-1 and μ s (L4) = 15.4 cm-1 and block optical properties are μ a (B3) = 0.147 cm-1 and μ s (B3) = 9.3 cm-1. The data collected with channel b (r from 3.0 to 4.5 cm) have been normalized to match the data points acquired at r = 3.0 cm by channels a and b.

Fig. 5
Fig. 5

Summary of our results for all the 100 superficial-layer–underlying-block combinations examined. The black (gray) bars show the percentage deviation between the effective optical properties measured with channel a (channel b) in the presence of one layer, and the corresponding optical properties of the underlying block. The number at the top of each black–gray bar pair indicates the thickness of the layer in centimeters. The horizontal dashed lines indicate the errors. [The instrumental error in the relative deviation is ±10%. This error is increased to ±20% for μ s ′ in (b)–(d) to take into account the effect of the layer–block interface.] The thick horizontal lines indicate the relative deviations (when they are not zero) between the layer and the block optical coefficients. (a) The layer and the block have the same optical coefficients. (b) The layer and the block have the same absorption but different reduced scattering coefficients. (c) The layer and the block have the same reduced scattering but different absorption coefficients. (d) The layer and the block have different absorption and reduced scattering coefficients.

Fig. 6
Fig. 6

Normalized deviations of (a) the effective absorption and (b) the reduced scattering coefficients from the corresponding block values. The symbols indicate the experimental results when the optical properties of the layer and the block were different. The curves give an indication of the average trend of the data points. These normalized deviations assume values of 0 and 1 when the measured effective coefficients coincide with those of the block and the layer, respectively. Horizontal axis, ratio between the thickness of the superficial layer (t) and the average effective photon penetration depth 〈zeff calculated from Eq. (1). In the limit of very thin layers (t → 0), the normalized deviations tend to 0, indicating that we measure the optical properties of the underlying block. In the limit of a very thick superficial layer (t → ∞), the normalized deviations tend to 1, indicating that we measure the optical properties of the layer.

Fig. 7
Fig. 7

Symbols represent the difference between the effective absorption coefficients measured with the precalibrated method on one layer from batch 1 on top of block 3 and on the same layer on top of block 1. Different symbols refer to different layer thicknesses. The horizontal line at 0.076 cm-1 indicates μ a (B3) - μ a (B1).

Fig. 8
Fig. 8

Symbols represent the difference between the effective absorption coefficients measured with the DPF method on one layer from batch 1 on top of block 3 and on the same layer on top of block 1. Different symbols refer to different layer thicknesses. The horizontal line at 0.076 cm-1 indicates μ a (B3) - μ a (B1).

Fig. 9
Fig. 9

Comparison of the relative measurements of μ a (eff) provided by the frequency-domain multidistance method (r in the range 3.0–4.5 cm; squares), the frequency-domain pre-calibrated method (r = 4 cm; triangles), and the cw DPF method (r = 4 cm; circles). (a) Only the block is changed [horizontal line, Δμ a (B)]. (b) Only the layer is changed [horizontal line, Δμ a (L)]. The multidistance method accurately recovers the difference between the block optical properties [Δμ a (B) is 0 in (b)] even in the presence of a superficial layer as much as ∼0.6 cm thick.

Equations (9)

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z = 1 2 r 3 μ a μ s 1 / 2 1 / 2
f r ,   dc ,   μ a eff ,   μ s eff = rS dc μ a eff ,   μ s eff + K dc ,
h r ,   Φ ,   μ a eff ,   μ s eff = rS Φ μ a eff ,   μ s eff + K Φ ,
μ a eff = - ω 2 v S dc S Φ S Φ 2 S dc 2 + 1 - 1 / 2 ,
μ s eff = S dc 2 3 μ a - μ a ,
ln I 0 / I = μ a DPF r + G .
μ a 2 eff - μ a 1 eff = 1 r DPF ln I 1 / I 2 .
μ a eff - μ a B μ a L - μ a B ,
μ s eff - μ s B μ s L - μ s B ,

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